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CPS1915 Han G. et al.
            where   denotes an input feature vector, and  ,  and  ,  denote the
                    
            maximum and minimum in the   input vector, respectively.
                                            ℎ

            3.  Result
                The experiments were all performed using Python 3.7 and Sklearn library,
            which relies on Numpy, Scipy, and matplotlib, and conducted in a Linux server
            with an Intel Core i7 2.2 GHz processor. The neural network models for the
            bank telemarketing data included one input layer with 20 input features and
            output  layer  with  one  node.  The  optimal  size  of  the  hidden  layer  was
            determined by tuning the number of nodes. The number of choice ranges
            from 0 to 50. The number of iteration was set to be 10000 for all experiments.
            The initial value of the learning rate is 1.2. Due to the limited space, the table
            for the prediction accuracy values failed to show in the text which is available
            from the corresponding author.
                In Model I, the best prediction performance (71.72%) occurred when the
            hidden  layer  with  20  neurons  while  the  worst  performance  (57.21%)  was
            obtained when the number of hidden neuron is 2. In Model II, the best and
            worst performance occurred when the number of hidden neurons were 44 and
            3, respectively. The accuracy trend for Model II is more stable whereas Model
            I has two sharp declines in the number of 2 and 15 of hidden neurons. The
            trendlines for Model I and Model II demonstrate that the more the hidden
            units, the better the model fits the data, which embodied more obviously for
            Model II (see Figure 3).
























                        Figure 3. Prediction accuracy for Model I and Model II
                Confusion matrix is a simple but powerful tool to evaluate the classification
            performance. It contains four values, such as true negative (TN), false positive
            (FP), false negative (FN) and true positive (TP). Table 1 showed the confusion
            matrix of Model I when the number of hidden layer neuron was 20.


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